Adding and Subtracting Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

How do you add rational functions with different denominators?

Back

To add rational functions with different denominators, find a common denominator, rewrite each function with that denominator, and then combine the numerators.

Front

What is the first step in subtracting rational functions?

Back

The first step in subtracting rational functions is to find a common denominator.

Front

Define 'common denominator'.

Back

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be combined.

Front

What does it mean to simplify a rational function?

Back

Simplifying a rational function means reducing it to its lowest terms by factoring and canceling common factors in the numerator and denominator.

Front

What is the process of factoring in rational functions?

Back

Factoring in rational functions involves rewriting the numerator and/or denominator as products of their factors to simplify the expression.

Front

How do you determine the least common denominator (LCD) of two rational functions?

Back

To determine the least common denominator (LCD), factor each denominator and take the highest power of each factor present.

Front

What is the significance of identifying restrictions in rational functions?

Back

Identifying restrictions is important because it determines the values for which the rational function is undefined, typically where the denominator equals zero.

Front

Provide an example of adding two rational functions: (1/x) + (1/y).

Back

The sum is (y + x) / (xy).

Front

Provide an example of subtracting two rational functions: (3/x) - (2/x^2).

Back

The result is (3x - 2) / (x^2).